Object classification in digital images remains one of the most challenging tasks in computer
vision. Advances in the last decade have produced methods to repeatably extract and describe
characteristic local features in natural images. In order to apply machine learning techniques
in computer vision systems, a representation based on these features is needed.
A set of local features is the most popular representation and often used in conjunction
with Support Vector Machines for classification problems. In this work, we examine current
approaches based on set representations and identify their shortcomings.
To overcome these shortcomings, we argue for extending the set representation into a
graph representation, encoding more relevant information. Attributes associated with the
edges of the graph encode the geometric relationships between individual features by making
use of the meta data of each feature, such as the position, scale, orientation and shape of the
feature region. At the same time all invariances provided by the original feature extraction
method are retained.
To validate the novel approach, we use a standard subset of the ETH-80 classification
benchmark.

New classification algorithms based on the notion of 'margin'
(e.g. Support Vector Machines, Boosting) have recently been developed.
The goal of this thesis is to better understand how they work, via a
study of their theoretical performance.
In order to do this, a general framework for real-valued
classification is proposed. In this framework, it appears that the
natural tools to use are Concentration Inequalities and Empirical
Processes Theory.
Thanks to an adaptation of these tools, a new measure of the size of a
class of functions is introduced, which can be computed from the data.
This allows, on the one hand, to better understand the role of
eigenvalues of the kernel matrix in Support Vector Machines, and on
the other hand, to obtain empirical model selection criteria.

This thesis presents a theoretical and practical study of Support
Vector Machines (SVM) and related learning algorithms. In a first part,
we introduce a new induction principle from which SVMs can be derived, but
some new algorithms are also presented in this framework.
In a second part, after studying how to estimate the generalization
error of an SVM, we suggest to choose the kernel parameters of an SVM
by minimizing this estimate. Several applications such as feature
selection are presented. Finally the third part deals with the incoporation
of prior knowledge in a learning algorithm and more specifically, we
studied the case of known invariant transormations and the use
of unlabeled data.

Our goal is to understand the principles of Perception, Action and Learning in autonomous systems that successfully interact with complex environments and to use this understanding to design future systems